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Displaying similar documents to “The automorphism group of the modular curve X 0 ( 63 ) ”

On equations defining fake elliptic curves

Pilar Bayer, Jordi Guàrdia (2005)

Journal de Théorie des Nombres de Bordeaux

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Shimura curves associated to rational nonsplit quaternion algebras are coarse moduli spaces for principally polarized abelian surfaces endowed with quaternionic multiplication. These objects are also known as . We present a method for computing equations for genus 2 curves whose Jacobian is a fake elliptic curve with complex multiplication. The method is based on the explicit knowledge of the normalized period matrices and on the use of theta functions with characteristics. As in the...

Singular values, Ramanujan modular equations, and Landen transformations

M. Vuorinen (1996)

Studia Mathematica

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A new connection between geometric function theory and number theory is derived from Ramanujan’s work on modular equations. This connection involves the function φ K ( r ) recurrent in the theory of plane quasiconformal maps. Ramanujan’s modular identities yield numerous new functional identities for φ 1 / p ( r ) for various primes p.